Lorentz Group in Optical Sciences

Click here for Einstein's photons.

Squeezed States!

Have you seen this picture?
It came from my papers.
Have you seen posters for the International Conference on Squeezed States and Uncertainty Relations?

The picture is for Lorentz-boosted extended objects in particle physics. The supporting mathematics is called the Lorentz group. This group, by now, is the standard mathematical device for quantum and classical optics.

It is by now widely established that the Wigner function is the key scientific language for quantum optics, but not many people know that those Wigner functions in optics also serve as the representation of the Lorentz groups, such as O(2,1) and O(3,2) which are the fundamental languages for the one- and two-mode squeezed states. When you do squeezed states, you are doing the Lorentz groups.

On this subject, with Marilyn Noz, I have written a book entitled Phase Space Picture of Quantum Mechanics.

Recently, I have been publishing papers on applications of the Lorentz group to classical ray optics, mostly in Phys. Rev. E. Those papers were also archived in Los Alamos. Some of them are listed below.

Indeed the Lorentz group covers the entire range of classical and quantum mechanics. We all know God created the light and the materials through which light waves propagate. If this is the case, God spoke the language of the Lorentz group.